Finite Group Databasebeta

← #28399416

Subgroups — #28399416

Order 14464.

470 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813654C211yesmaximal, characteristic
2#20299080C211yesmaximal, characteristic
3#20299074C211yesmaximal, characteristic, complemented
4#20298702C211yesmaximal, characteristic, complemented
5#20298701C211yesmaximal, characteristic, complemented
6#20298700C211yesmaximal, characteristic, complemented
7Q16×Dic113C211yesmaximal, characteristic, complemented
8C4×#14268637C211yesmaximal, characteristic, complemented
9C4×#14268634C211yesmaximal, characteristic, complemented
10#20298685C211yesmaximal, characteristic, complemented
11#20298637C211yesmaximal, characteristic, complemented
12#20298593C211yesmaximal, characteristic
13#103×D113C211yesmaximal, characteristic, complemented
14#20298555C211yesmaximal, characteristic, complemented
15#441×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18#16813654C418yescomplemented
19C2×#14268637C2211yescharacteristic
20C2×#14268636C2211yescharacteristic
21C2×#14268634C2211yescharacteristic
22C2×#14268630C2211yescharacteristic
23C2×C8×D113C2211yescharacteristic
24Q8×Dic113C2211yescharacteristic
25Q8×Dic113C2211yescharacteristic
26C4×Dic226—21no—
27C4×Dic226C2211yescharacteristic
28#16813587—21no—
29#16813587C2211yescharacteristic
30C4×D452—21no—
31C4×D452C2211yescharacteristic
32#16813584—21no—
33#16813584C2211yescharacteristic
34#16813580—21no—
35#16813580C2211yescharacteristic
36#16813579—21no—
37#16813579—21no—
38#16813579C2211yescharacteristic
39C4⋊C4×D113—21no—
40C4⋊C4×D113C2211yescharacteristic
41#16813556C2211yescharacteristic
42#16813555C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813544C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813532C2211yescharacteristic
51C4×#11744751C2211yescharacteristic
52C8×Dic113C2211yescharacteristic
53C2×Q16×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59#97×C113C2211yescharacteristic
60#14268648—22no—
61#14268648C2×C414yes—
62C2×Dic226—21no—
63C2×Dic226C2311yescharacteristic
64Q8×D113—22no—
65Q8×D113C2×C414yescomplemented
66C2×D452—21no—
67C2×D452C2311yescharacteristic
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113C2311yescharacteristic
74#14268637C2×C414yescomplemented
75#14268636C2×C414yescomplemented
76#14268634C2×C414yescomplemented
77#14268630C2×C414yescomplemented
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C8×D113—22no—
81C4⋊Dic113—21no—
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626D411yescharacteristic
89#14268626D411yescharacteristic
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624D411yescharacteristic
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113—21no—
97C4×Dic113—21no—
98C4×Dic113—21no—
99C4×Dic113—21no—
100C4×Dic113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C2×Q8×C113C2311yescharacteristic
103Q16×C113C2×C414yescomplemented
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C4⋊C4×C113—21no—
107C4⋊C4×C113—21no—
108C4⋊C4×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C42×C113—21no—
111C42×C113—21no—
112C42×C113C2311yescharacteristic
113C22×D113—21no—
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113C22×C412yes—
118Q8×C113C22×C412yes—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2411yescharacteristic
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132D452—24no—
133D452—21no—
134D452C22×C412yes—
135C4×D113—24no—
136C4×D113—24no—
137C4×D113—81no—
138C4×D113—81no—
139C4×D113—81no—
140C4×D113C22×C412yes—
141C4×D113#4112yes—
142Dic226—21no—
143Dic226—24no—
144Dic226C22×C412yes—
145C8×C113—21no—
146C8×C113C22×C412yes—
147#11744751—21no—
148#11744751C22×C412yes—
149C22×C113C22×D411yescharacteristic
150C2×D113—21no—
151C2×D113—21no—
152C2×D113—22no—
153C2×D113—41no—
154C2×D113—41no—
155C2×D113C4×D412yes—
156C4×C113—22no—
157C4×C113—22no—
158C4×C113—21no—
159C4×C113—21no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113C23×C411yescharacteristic
163C4×C113C2×#4111yescharacteristic
164Dic113—22no—
165Dic113—21no—
166Dic113—21no—
167Dic113—41no—
168Dic113—41no—
169Dic113C4×D412yes—
170C2×C113C2×C4×D411yescharacteristic
171C2×C113#57711yescharacteristic
172C2×C113#57811yescharacteristic
173D113—22no—
174D113—42no—
175#2947—1131nomaximal, Sylow
176C113#294711yescharacteristic, complemented, Sylow
177C2×#137—1131no—
178#520—1131no—
179#519—1131no—
180#441—1131no—
181#441D11311yescharacteristic, complemented
182#440—1131no—
183#440—1131no—
184C4×Q16—1131no—
185C4×Q16—1131no—
186C4×SD16—1131no—
187C4×SD16—1131no—
188#428—1131no—
189#416—1131no—
190C2×#103—1131no—
191#405—1131no—
192C2×#41—1131no—
193C22×Q8—1131no—
194#137—1138no—
195C2×Q16—1131no—
196C2×Q16C2×D11311yescharacteristic
197C2×SD16—1131no—
198C2×SD16—1131no—
199C2×M16—1131no—
200C22×C8—1131no—
201C4×Q8—1131no—
202C4×Q8—1131no—
203C4×Q8—1131no—
204C4×Q8—1131no—
205C4×Q8—2261no—
206C4×Q8—2261no—
207C4×Q8C2×D11311yescharacteristic
208C4×Q8C2×D11311yescharacteristic
209C4×D4—1131no—
210C4×D4—1131no—
211C4×D4—2261no—
212C4×D4—2261no—
213#117—1131no—
214#117—1131no—
215#117—2261no—
216#117—2261no—
217#117—2261no—
218C2×C4⋊C4—1131no—
219C2×C4⋊C4—2261no—
220#107—1131no—
221#107—1131no—
222#106—1131no—
223#106C2×D11311yescharacteristic
224#103—1131no—
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#103C2×D11311yescharacteristic
229#103C2×D11311yescharacteristic
230#102—1131no—
231#102—1131no—
232#97—1131no—
233#97C2×D11311yescharacteristic
234C4×C8—1131no—
235C4×C8—1131no—
236#41—1134no—
237#41—2262no—
238C2×Q8—1134no—
239C2×Q8—1131no—
240C2×Q8—2261no—
241C2×Q8—2262no—
242C2×Q8C22×D11311yescharacteristic
243C2×Q8C22×D11311yescharacteristic
244C2×D4—1131no—
245C2×D4—2261no—
246C22×C4—1131no—
247C22×C4—2261no—
248C22×C4—2261no—
249C22×C4—2261no—
250C22×C4—2261no—
251C22×C4—2261no—
252Q16—1134no—
253Q16C4×D11314yescomplemented
254SD16—1134no—
255SD16—1134no—
256M16—1134no—
257C2×C8—1131no—
258C2×C8—1131no—
259C2×C8—2262no—
260C2×C8C22×D11311yescharacteristic
261C2×C8C22×D11311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—1131no—
265C4⋊C4—1131no—
266C4⋊C4—1131no—
267C4⋊C4—1131no—
268C4⋊C4—2261no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4C22×D11311yescharacteristic
274C4⋊C4C22×D11311yescharacteristic
275C22⋊C4—1131no—
276C22⋊C4—1131no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C42—21no—
281C42—21no—
282C42—1131no—
283C42—2261no—
284C42—2261no—
285C42—2261no—
286C42—2261no—
287C42—2261no—
288C42C22×D11311yescharacteristic
289C23—1131no—
290C23—2261no—
291Q8—21no—
292Q8—21no—
293Q8—1132no—
294Q8—2264no—
295Q8—2261no—
296Q8C2×C4×D11312yes—
297Q8C2×C4×D11312yes—
298D4—1132no—
299D4—2264no—
300D4—2261no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—1131no—
306C2×C4—1132no—
307C2×C4—1132no—
308C2×C4—1131no—
309C2×C4—1131no—
310C2×C4—9041no—
311C2×C4—9041no—
312C2×C4—9041no—
313C2×C4—2264no—
314C2×C4—2264no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4D4×D11311yescharacteristic
319C2×C4D4×D11311yescharacteristic
320C2×C4C23×D11311yescharacteristic
321C8—21no—
322C8—1132no—
323C8—2261no—
324C8C2×C4×D11312yes—
325C22—1132no—
326C22—4521no—
327C22—4521no—
328C22—2262no—
329C22—2261no—
330C22—2261no—
331C22C2×D4×D11311yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—1132no—
339C4—4521no—
340C4—4521no—
341C4—2262no—
342C4—2261no—
343C4—2261no—
344C4C22×C4×D11311yescharacteristic
345C4#41×D11311yescharacteristic
346C2—4522no—
347C2—2262no—
348C2C4×D4×D11311yescharacteristic
349C2#2029940711yescharacteristic
350C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
Fitting#441×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268648C22
cosocleC2×C4×C113C24
hypercenter#441D113
hypocenterC113#2947
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #20299074C2semidirect
4. #20298702C2semidirect
5. #20298701C2semidirect
6. #20298700C2semidirect
7. Q16×Dic113C2semidirect
8. C4×#14268637C2semidirect
9. C4×#14268634C2semidirect
10. #20298685C2semidirect
11. #20298637C2semidirect
13. #103×D113C2semidirect
14. #20298555C2semidirect
15. #441×C113C2semidirect
18. #16813654C4semidirect
65. Q8×D113C2×C4semidirect
74. #14268637C2×C4semidirect
75. #14268636C2×C4semidirect
76. #14268634C2×C4semidirect
77. #14268630C2×C4semidirect
103. Q16×C113C2×C4semidirect
176. C113#2947semidirect
181. #441D113semidirect
253. Q16C4×D113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168136542
#202990802
#202990742
#202987022
#202987012
#202987002
Q16×Dic1132
C4×#142686372
C4×#142686342
#202986852
#202986372
#202985932
#103×D1132
#202985552
#441×C1132
#2947113